In their study of infinite flag varieties, Lam, Lee, and Shimozono (2021) introduced bumpless
pipe dreams in a new combinatorial formula for double Schubert polynomials. These …

Geometric vertex decomposition and liaison are two frameworks that have been used to
produce similar results about similar families of algebraic varieties. In this paper, we …

Schubert patch ideals are a class of generalized determinantal ideals. They are prime
defining ideals of open patches of Schubert varieties in the type A flag variety. In this paper …

Bipartite determinantal ideals are introduced in Illian and Li (Gröbner basis for the double
determinantal ideals, http://arxiv. org/abs/2305.01724) as a vast generalization of the …

A major open question in the theory of Gorenstein liaison is whether or not every
arithmetically Cohen-Macaulay subscheme of $\mathbb {P}^ n $ can be G-linked to a …

Nakajima's graded quiver varieties naturally appear in the study of bases of cluster algebras.
One particular family of these varieties, namely the bipartite determinantal varieties, can be …

Grobner bases are an important tool for working with ideals in polynomial rings. They have
both computational and theoretical importance. In this dissertation, we produce Grobner …

Nagel and Römer introduced the class of weakly vertex decomposable simplicial
complexes, which include matroid, shifted, and Gorenstein complexes as well as vertex …

Commutative algebra stands as a dynamic domain in mathematical research,
interconnected with various disciplines. Its classical roots lie in algebraic geometry and …

We examine Li's double determinantal varieties in the special case that they are toric. We
recover from the general double determinantal varieties case, via a more elementary …